Finite Group DatabasebetaFinite Group Databasebeta| order | 24567 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C431 · Schur multiplier (H2) = C1 |
| direct product | C19⋊C3×C431 |
| unambiguous semidirect product | C19⋊(C3×C431) |
| unambiguous semidirect product | (C19×C431)⋊C3 |
| Fitting, socle, Hall | C19×C431 ⋊ C3 |
| derived, Sylow | C19 ⋊ C3×C431 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C431 | C19⋊C3 |
| commutator, cosocle, hypocenter | C19 | C3×C431 |
| Frattini | C1 | G |
| Fitting, socle | C19×C431 | C3 |
| LCS | G ▷ C19 | |
| UCS | C1 ◁ C431 | |
8 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8189 |
3879 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(24567, 1);